An Energy Efficiency Power and Sub-carrier Allocation for the Downlink Multi-user CoMP in Multi-Cell Systems Xiaoliang Zhang, Yi Li and Hong Ji Key Laboratory of Universal Wireless Communications, Ministry of Education Beijing University of Posts and Telecommunications Beijing, P.R.China Email:
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[email protected] Abstract — Coordinated multi-point transmission/reception (CoMP) has been proposed as an effective technology to improve cell-edge throughput in next-generation wireless systems. However, all the BSs(Base Station) need to share all the users’ messages to do the global precoding for supporting each user best service, such as which BS will be chosen for cooperating or how to realize the cooperation, lots of energy will be consumed when doing this process. In addition, in most of the exsiting works, BSs always allocate equal power to all the users neglecting user’s Channel State Informations(CSIs) or their service requirements, this may also cause enery wasting. In this paper, we focus on the throughput maximizing problem while fully considering energy saving problem in the CoMP systems. At first, we propose the concept of “cell zooming” which we define that one of the cooperating BSs will “sleep” if it improves little to user’s service, then a sub-carrier allocation algorithm with varying power assignment in downlink CoMP system is put forward, this can lower the transmit power of BS. We formulate that the sub-carrier and power allocation problem is a mixed binary integer programming (MBIP) problem, a “green” subcarrier and power allocation algorithm which can maximize the cell’s throughput is proposed at last, the power allocated to each user will be calculated. Simulation results show that the proposed sub-carrier and power allocation algorithm is much better on users’ throughput and fairness while consumes less energy than the existing ones. Keywords-CoMP, energy saving, throughput, power allocation
I. INTRODUCTION In modern times, the idea of green and energy-saving networking problem has begun to attract more and more people’s discussion, the low carbon awareness is deeply rooted in people’s daily life, study and work now. But as more and more people are using the mobile phones and the diversification of service that the mobile phone can provide, not only the Base Station (BS) have to deal with more and more users’ messages to make the correct decision and send the correct instruction, but also the mobile phone’s powerful function need to exchange amounts of signaling with the BS, both of the above process need to consume more and more energy[1]. Though the telecom operators upgrade their devices all the time, in some counties they even build the next This paper is jointly sponsored by the Ministry of Industry and Information Technology of the People’s Republic of China (2011ZX03001-007-03), the Nature Science Foundation of Beijing under Grant 4102044, and the National Science Foundation for Young Scientists of China under Grant 61001115.
generation network, the network electrical requirement is still continuous growing with an alarming trend. The LTE-Advanced system aims to solve the problem of low spectral efficiency of the cell edge. One of its main techniques—CoMP (coordinated multiple point transmission /reception) is proposed in [2]. Multiple eNode Bs(eNBs) in different cells can provide the same data to one user in a cooperative way on the same sub-carrier, the cell-edge users’ throughput is improved while the ICI can be avoided effectively[3][4]. But before doing this, all the eNBs in the whole cells will exchange all their Channel State Informations(CSI) and then decide which eNBs will solve the user coordinately. It will consume much energy during this process. Lower the transmit power of the BS can also decrease the consuming energy, if there are few users in the cell-edge areas, the BS can lower its transmit power and just ensure the service of the hot areas only. Different from the traditional network architecture, the LTE-A mainly focus on the celledge users, either the technology of Beamforming or the CoMP mainly aims to improve the Cell-edge users’ service, but both of them won’t consider the energy saving problem. In the existing papers [5], the power allocated to the each user is assumed to be equal whether the user with a good or bad CSI and then get the SINR target of the served user in order to solve the real-time near-optimal resource allocation of the uplink/downlink transmission. In this paper, we consider a suboptimal sub-carrier and power allocation algorithm combined CoMP with OFDMA in a multi-cell system, the problem of energy saving problem is considered by the algorithm. The cell’s throughput and user’s fairness can both be effectively improved while the power allocated to each user will be calculated. The main constructive work of this paper is as follows: We fully consider the energy-saving problem and propose a concept of “cell-zooming” which means that if one of the cooperating eNBs provides little help for improving the user’s service, the eNBs will lower its transmit power and reduce the cell’s coverage, for the cell edge users , it means that the eNBs “sleep”.
Figure 2. The frequency band allocated to each cell
B. The optimal problem Figure 1. The cell layout of multi-cell system
After the cooperated cells are determined, a suboptimal sub-carrier allocation algorithm which considers all the users’ fairness is proposed, after all the sub-carriers are assigned to the users, the power assigned to each user is calculated in the end. This paper is organized as follows. In the next section, we present the wireless network model of resource allocation and formulate the optimal problem. In Section III, we describe our sub-carrier and power assignment algorithm. In Section IV, we give the simulation results of this algorithm and compare them with the results of two existing algorithms. In Section V, we provide our conclusion and final remarks.
Therefore the optimization problem which is to maximize all the users’ throughput in one sector under constraint conditions can be formulated as follows:
max
pu ,n , u ,n
U1 U2 N
U1 U 2 N
u 1
PROBLEM A. Network and channel models
N
Ru u , n log 2 (1 n 1
pu ,n hu , n n0
2
), u U A U B
(1)
(3)
n 1
u ,n
pu , n P
(4) (5)
u , n 0,1 , u, n
(6)
u 1
Let hukn denote the vector of channel gains of user u in sector k on sub-carrier n . Assuming the transmit power on subcarrier n in each sector is pu , n , the unit bandwidth capacity of user u can be expressed as
)
pu , n 0, u, n
WIRELESS NETWORK AND OPTIMAL
Considering a multi-cell OFDM system composed of K 3 cells ( K sectors), three adjacent sectors which belong to different cells form a new “cell”, we call it a “cluster”, such as the yellow hexagon of Fig.1. Each cluster has a bandwidth of W which is not overlapped and equally divided into N subcarriers, such as Fig.2.
n0
2
Subject to
U1 U 2
II.
log2 (1
u,n
u 1 n 1
pu ,n hu,n
u , n 1, n
(7)
Ru RAmin , u U A
(8)
Ru R
(9)
min B
Ru
Ri
, u U B
u , u U A U B
(10)
（U A U B） i
The constraint condition (4) means that the total power can be allocated to all the users in one sector. The constraint condition (6) denotes that whether a sub-carrier n is occupied by user u .The constraint condition (7) guarantees each subcarrier can only be assigned to one user. The constraint condition (8) and (9) ensure that the CoMP user and Cellcenter user’s minimum rate respectively. The constraint (10) ensures that the CoMP user and Cell-center users’ fairness to occupy the best sub-carrier[6]. III.
HEURISTIC SUBOPTIMAL SUB-CARRIER AND
User u will be divided into two classes according to its SINR . If SINRu , where is a predetermined threshold, user u is considered to be a CoMP user, otherwise is considered to be a Cell-center user. The CoMP users and Cell-center users are denoted by U A and U B respectively, where U A 1, 2,U1 ,
POWER ALLOCATION In this section, we will propose a suboptimal sub-carrier and power allocation algorithm to maximize all the users’ throughput while the energy-saving problem is considered. Before it, an optimal algorithm will be analyzed.
U B 1, 2,U 2 . The white Gaussian noise n0 is thought to
A. Heuristic Optimal Sub-carrier and Power Allocation
be the same on all sub-carriers. u , n 1 means that the sub-
Because the optimization problem is a mixed binary integer programming(MBIP) problem as the objective function (3) has
carrier n is allocated to user u , otherwise u , n 0 .
U S U M U1 .The detailed flow of our sub-carrier allocation algorithm is shown as follows:
Algorithm 1 Suboptimal Sub-carrier Allocation Algorithm Step 1:Initialization: Let Ru =0 , u1 = , u2 = , C1 = 1, 2， , N , C2 = 1, 2， , N .
Step 2: In sector C1 ：For u 1 to U S U 2 , do
a) Calculate Gu , n and find n arg max Gu , n n C1
b) Figure 2.
BS sleeping and neighboring BSs transmit cooperatively
the discrete binary index u , n , the optimization problem (3) can’t use the traditional convex optimization method directly to get the optimal solution as it is not a convex optimization problem, but we can propose an optimal algorithm to realize the optimal sub-carrier and power allocation for all the users as follows. We firstly exhaustively search over all possible subcarriers combination for all the users. Then for each combination, we can calculate the power allocated to each user under the constraints condition. Finally, we can get the optimal combination from all the possible combinations. However, the optimal algorithm is too complex.
B.
Suboptimal Sub-carrier Allocation for All the Users
While user u is a CoMP user, it can select the other two sectors of one cluster for cooperating. Considering the energy saving problem, if one sector helps little for user u ’s service, the eNBs will lower its transmit power and will “sleep” for user u ,such as Fig.3. It means that one of the coordinated sectors will not be selected, the other two sectors will work for user u together. The two active eNBs will allocate sub-carrier to user u for transmitting data cooperatively. When user u is a Cell-center user, the eNBs in each sector will serve the user respectively. The SINR of user u located in cluster m which includes sector m1 , m2 , m3 on sub-carrier n is SINRum1 , m2 , m3 , if it satisfies: m1 , m2 , m3 u m2 , m3 u
SINR (11) max( SINR , SINR , SINRum1 , m3 ) where the superscripts of SINR mean the selected coordinated sectors, is a predetermined threshold, then the cooperated sectors will be chosen by: u arg max( SINRum1 , m2 , SINRum2 , m3 , SINRum1 , m3 ) (12) Next we will propose a suboptimal sub-carrier allocation algorithm for the whole users. We first assume the power is allocated equally to all idle sub-carriers and let the subcarrierm1 , m2 u
to-noise ratio is Gu , n hu , n
2
n0 , we suppose the Cell-center
users in Sector C1 and Sector C2 are the same, denoted by U C1 1, 2,U S and U C2 1, 2,U M ,where U S =U M and
Let u1 =u1 +n and C1 = C1 -n
In sector C2 ：For u 1 to U M U 2 , do c)
Calculate Gu , n and find n arg max Gu , n
d)
Let u2 =u2 +n and C2 = C2 -n
n C2
then calculate the capacity Ru for u U A U B as (1). Step 3: In sector C1 :For u U C1 U A , while C1 ,do
a) Find the user u arg min Ru u
b) Find the n arg max Gu , n n C1
c)
Let u =u n and C1 = C1 -n for the 1
1
selected u and n ,and calculate Ru as(1) , u u u
Step 4: In sector C2 :For u U C2 U A , while C2 ,do
d) Find the user u arg min Ru u
e)
Find the n arg max Gu , n
f)
Let u =u n and C2 = C2 -n for the
n C2
2
2
selected u and n ,and calculate Ru as(1) , u u u
Step 5: Calculate Ru , u U A , u =u u , forward to 1
2
step 3. In this algorithm, we will allocate the best sub-carrier to users with best Gu , n either in sector C1 or in sector C2 , as all the CoMP users in a cluster are served by two eNBs in sector C1 and C2 , the throughput Ru , u U B will be determined by two eNBs. Considering the fairness, we will choose the best sub-carrier from residual sub-carriers and assign it to the user with worst Ru , and then we will repeat this process until all the sub-carriers are assigned to the users. C. Optimal Power Allocation for All the Users Based on the algorithm 1, we let u denote the set of
sub-carriers assigned to the user u ,where u {1, 2， Nu } . Now we can do the optimal power allocation for each user and the optimization problem will be written: max
U1 U 2
pu ,n
u 1 n u
log 2 (1 pu , n Gu , n )
know that the power allocated to user u on sub-carrier n is determined by Gu , n , Gu , n is known to us. Then let U1 U 2
(13)
u 2
ln 2 u 1 u 1 u
The optimization problem (13) is still complex for the constraint condition (10). However, according to [7], we can rewrite the last constraint condition equivalently as (14) R1 : R2 : : RU1 U 2 1 : 2 : : U1 U 2 ，u U A U B Now relying on [8], the optimization problem (3) is equivalent to solve the following Lagrangian dual problem L(, u ,u , u , p1, n , pu, n )
U1 U2
log (1 p u 1 nu
2
u,n
Gu,n ) ( p
U1 U2
p
u,n
u 1 nu
G1, n L 1 1 + p1, n ln 2 1 p1, n G1, n
U1 U 2
u 2
(15)
u 2
ln 2
u , n 1 (17)
(19)
1 , n 1 G1, n
(20)
log n 1
2
(1 pu , n Gu , n ) RAmin
(21)
The equation (21) can further be expressed as min
(1 pu ,1Gu ,1 )(1 pu ,2 Gu ,2 ) (1 pu , Nu Gu , Nu ) 2 RA U1 U 2
As
u 1 u 1 u ，u 2 and ln 2 u
u 2
u 1 1 ln 2
(26)
(22)
，u 1
are invariant when given a user u , from (19) and (20) we
(27)
Then we expand the equation (28), we can get (28)
Since (28) is an equation of higher degree, if N u is an odd, the equation has at least one solution, if N u is an even, the power allocation pu , n , u 2 will be got. For u 1 , we substitute (25) into (22) and get, (1 Z1 G1,1 )(1 Z1 G1,2 ) (1 Z1 G1, Nu ) 2 RA , u =1
(29)
According to (29), we can get the power allocation p1, n . Although the power allocation pu , n and p1, n will be got while we get the solution of Z and Z1 , but since Z and Z1 may have more than one solution respectively, so we have to find one solution to get the optimal power allocation. In the same way, we can also calculate the power allocated to the Cell-center user pu , n when u 2 and p1, n when u =1 for u U B . We can get the total power assigned to all the users as follows: U1 Nu
N1
U1 Nu
Ptotal Z1 G1,n Z Gu ,n Z1 G1,n Z Gu ,n (30) n 1 u 2 n 1 n 1 u 2 n 1 uU A
But in (19) and (20), we can’t calculate the Lagrangian multiplier factors , u , 1 , u , then we let (16) equal to 0 and get Nu
pu , n Z Gu , n , n u , u 2
Substitute (26) into (22), we can get
N1
(25)
min
u 1 u 1 u Gu , n , n u ln 2 u While u 1 , we let (17) equal to 0 and get p1, n
p1, n Z1 G1, n , n Z1 , u =1
min
(16)
pu , n
u 1 1
(24)
+Gu ,1 Gu , Nu2 Gu , Nu ) Z Nu 1 1 2RA ，u 2
CoMP users, for u U A , u 2 , we let (18) equal to 0 and get
Z
Gu ,1 Gu ,2 Gu , Nu Z Nu (Gu ,1 Gu ,3 Gu , Nu Gu ,2 Gu ,3 Gu , Nu
Gu , n 1 1 L 1+u u , n u (18) u pu , n ln 2 1 pu , n Gu , n At first we will get the optimal power allocation Pu , n for
U1 U 2
(23)
min
Where , u , u , u are the Lagrangian multiplier factors. For u U A , we differentiate (15) and get L log 2 (1 pu , n Gu , n ) RAmin u n u
ln 2 u
=Z1
(1 Z Gu ,1 )(1 Z Gu ,2 ) (1 Z Gu , Nu ) 2 RA , u 2
)
U1 U2 u log2 (1 pu,nGu, n ) RAmin u log2 (1 pu,nGu,n ) RBmin u 1 nu u 1 nu U1 U2 1 u log2 (1 p1,nG1, n ) log2 (1 pu,nGu, n ) u nu u 2 n1
u 1 1
uU B
The optimal power allocation pu , n can be got when the optimal solution of Z and Z1 for u U A as well as Z and Z1 for u U B are found to make Ptotal minimized, in addition, according to the constraint condition (4), Ptotal must be no more than P . SIMULATION RESULTS IV. In this section, we will give the simulation results of three different sub-carrier allocation and power allocation algorithms: the existing algorithm, the proposed algorithm and the algorithm 1. The existing algorithm: the eNBs will not distinguish the Cell-center users and the CoMP users and the eNBs’ transmit power is unchanged with its size is fixed too. The algorithm 1 means three active eNBs serve one CoMP
400
The Exsiting Algorithm The Proposed Algorithm The Algorithm 1
300 Normalized energy consumption(w)
350 Normalized energy consumption(w)
350
U1+U2=10 U1+U2=20 U1+U2=30
300 250 200 150 100
250
200
150
100
50 0 0.1
50 0.1
0.2
0.3
0.4
0.5 0.6 U1/(U1+U2)
0.7
0.8
0.9
0.2
0.3
0.4
0.5 0.6 U1/(U1+U2)
1
V. CONCLUSION In this paper, we proposed a “green” sub-carrier and power allocation algorithm combined with CoMP, the problem of energy saving problem is well considered. The power allocated to each user is calculated while the throughput of all the users is maximized. Simulation results are presented to demonstrate that the performance of the proposed algorithm is superior to the existing ones.
0.8
0.9
1
Fig. 4. The energy consumed for users when U1+U2=20
Fig.3. Total energy consumption for different number of users
3
The Exsiting Algorithm The Proposed Algorithm The Algorithm 1
2.5
Throughput(bit/s/hz)
user cooperatively and the cell’s coverage is fixed, the eNBs allocate the sub-carriers to the users randomly, whether the user is a CoMP user or a Cell-center user. In Fig.3, we give the simulation results of energy consumption of this algorithm. We suppose that the active eNBs with power consumption P a and the sleeping eNBs with power consumption P s , where P a is usually much larger than P s . Suppose P a =400w, P s =10w, if the eNBs is “sleeping”, it will work for the Cell-center users of the sector only. From Fig.3, we know that as the number of the CoMP users is increasing, the energy consumed is growing, this is because that as the CoMP users is growing , the active eNBs need to increase its transmit power to meet the CoMP users’ power requirements, so the energy consuming is growing . In Fig.4, we give the simulation results of energy consumption of this algorithm compared to the other two algorithms. In algorithm 1, the transmit power is not varying, so the energy consumed is fixed. In the proposed algorithm, as one of the eNBs is “sleeping”, the energy consumed is less than the algorithm 1.When the number of CoMP users is small, the energy consumed of both the algorithm 1and the proposed algorithm is lower than the existing algorithm. In Fig.5, we illustrate the performance of the total throughput over different power constraints of the three different algorithms. In the simulation, we assume that there are 4 users, 6 idle sub-carriers and U1 U 2 1 . In the figure, we know that the whole throughput of the proposed algorithm is better than the existing algorithm as the cell-edge throughput is increased by the eNBs cooperating, but because the Cell-edge users will occupy the best sub-carrier, so the whole throughput of the proposed algorithm will be smaller than the algorithm 1.
0.7
2
1.5
1
0.5 0.1
0.2
0.3
0.4
0.5 0.6 Total Power(w)
0.7
0.8
0.9
1
Fig5. Total throughput for the whole users
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